Step 1: What you need
For a bike touring trip you don't need much gear. Of course you'll need a bicycle, but you don't need the best bicycle ever. If you already have a good everyday bicycle you use for most trips that would be sufficient. Make sure your brakes and gears work and take that thing to a shop for a tune up before you get on the road. Many cyclists would have you believe that you need fancy gear or clothing to do long distance rides, this is just not true!
Essentials for any road trip by bike are a few tools, patch kit, pump and tubes.
Next you need a way to haul your gear, the best way to do this is a bike rack and panniers. I have tried many types of panniers (and have even built my own) and the brand that i like the best are called panpack. The great thing about panpack is that they turn into a camping backpack when not in pannier form very useful. Any panniers that can carry the gear you need will work. If you get into having more gear a good bike trailer is a worthwhile investment.
The final consideration is based on how long your trip is. A well tuned rider can average about 60 miles a day no sweat. if you want to do longer rides or take it slower, you will need to plan for overnight. Bringing a small tent and sleeping bag is ideal. Food is also important, i find that i do better with high density foods like nut butters and rice dishes for those rides but if your ride is along civilization, pack lightly and fill up when need be.
I bring at least a day worth of clothes, a sweater, a bar of soap and changes of socks so i can feel a bit fresh.